Question

write the binomial probability in words. then, use a continuity correction to convert the binomial probability to a normal distribution probability.
p(x = 133)
write the probability in words.
the probability of getting 133 successes.
which of the following is the normal probability statement that corresponds to the binomial probability statement?

Explanation:

Step1: Write binomial probability in words

In binomial distribution, \(x\) represents the number of successes. So, \(P(x = 133)\) is the probability of getting exactly 133 successes.

Step2: Apply continuity correction

For a binomial random variable \(x\) approximated by a normal random variable \(X\), when \(P(x=k)\) (exact value for binomial), the continuity - corrected normal probability is \(P(k - 0.5<X<k + 0.5)\). Here \(k = 133\), so the normal probability is \(P(132.5<X<133.5)\)

Answer:

The probability of getting exactly 133 successes. The normal probability statement is \(P(132.5 < X<133.5)\)